Pattern method for higher harmonics from macromolecular orientation in oscillatory shear flow

Abstract

For a suspension of rigid dumbbells, in any simple shear flow, we must first solve the diffusion equation for the orientation distribution function by a power series expansion in the shear rate. Our recent work has uncovered the pattern in the coefficients of this power series [L. M. Jbara and A. J. Giacomin, “Orientation distribution function pattern for rigid dumbbell suspensions in any simple shear flow,” Macromol. Theory Simul. 28, 1800046-1–1800046-16 (2019)]. Specifically, we have here used this pattern on large-amplitude oscillatory shear (LAOS) flow, for which we have extended the orientation distribution function to the 6th power of the shear rate. In this letter, we embed this extension into the Giesekus expression for the extra stress tensor to arrive at the alternant shear stress response, up to and including the seventh harmonic. We thus demonstrate that the pattern method for macromolecular orientation now allows our harmonic analysis to penetrate the shear stress response to oscillatory shear flow far more deeply than ever.